These numbers arise out of approximations of nature.
360 is pretty darn close to the 365 days it takes for the Earth to revolve around the Sun, but has the advantage of being much more readily divisible into smaller parts. The prime factors of 365 are five and 73: that’s not very convenient for dividing up a year into smaller chunks; 360’s prime factors are two, three, and five. That creates a lot more flexibility.
Given the number of lunar cycles in a year, it makes some sense as to why night and day might be divided into two sets of 12 segments.